To convert the Cartesian equation y = 5 into a polar equation, we start by recalling the relationship between Cartesian coordinates (x, y) and polar coordinates (r, θ). In polar coordinates, we have:
- x = r × cos(θ)
- y = r × sin(θ)
Substituting the polar form of y into the Cartesian equation, we get:
r × sin(θ) = 5
To express this in a standard polar form, we can isolate r:
r = rac{5}{sin(θ)}
This equation shows how for every angle θ, the distance r from the origin maintains a constant y-coordinate of 5. Thus, the polar equation for the curve represented by the Cartesian equation y = 5 is:
r = rac{5}{sin(θ)}
So, we have derived the polar equation corresponding to that horizontal line in the Cartesian plane.